根據(jù)矩陣方程理論和細(xì)胞自動機(jī)原理，提出了加性細(xì)胞自動機(jī)狀態(tài)轉(zhuǎn)移結(jié)構(gòu)的同構(gòu)性方法，該方法利用狀態(tài)轉(zhuǎn)移矩陣方程及其特征多項(xiàng)式分析規(guī)則90和150加性細(xì)胞自動機(jī)，證明了特征多項(xiàng)式為不可約多項(xiàng)式時的零邊界規(guī)則90和150加性細(xì)胞自動機(jī)與其對應(yīng)的線性細(xì)胞自動機(jī)具有相同結(jié)構(gòu)的狀態(tài)轉(zhuǎn)移圖，即它們同構(gòu)。研究表明：該方法對實(shí)際的偽隨機(jī)序列產(chǎn)生、通信和測試等領(lǐng)域具有應(yīng)用推廣價值。
關(guān) 鍵 詞 加性細(xì)胞自動機(jī); 特征多項(xiàng)式; 狀態(tài)轉(zhuǎn)移圖; 同構(gòu)性

Abstract From the matrix theory and cellular automata theory, this paper presented the homogeneous characteristic methodology of cellular automata. The methodology utilized the state transition matrix equation and its characteristic polynomial to analyze the rule 90 and 150 additive cellular automata, and proved that if the characteristic polynomial of null boundary rule 90 and 150 linear cellular automata is non-dividable, then the states transition diagrams of the null boundary rule 90 and 150 additive cellular automata responding to the linear cellular automata have identical structure, while have different states. Research indicates that this methodology have advantages in the application fields of pseudorandom sequence generation, communications, and test.
Key words additive cellular automata; characteristic polynomial; state transition diagram; homogeneous characteristic